Publication
We investigate the conditions for the local arrest of a hydraulic fracture encountering a region of larger toughness. The propagation of a hydraulic fracture strongly depends on the ratio between the energy dissipated in the creation of new fracture surfaces and the energy dissipated in viscous flow. Because this ratio evolves during propagation, a hydraulic fracture can exhibit different behaviors when encountering the same toughness heterogeneity. The fracture can be locally arrested or its velocity only reduced. When viscous fluid flow dissipation dominates, a larger increase of fracture toughness is required to locally arrest the fracture. In the framework of linear hydraulic fracture mechanics, we determine the conditions under which a region of higher fracture toughness is capable of arresting a propagating hydraulic fracture. In particular, we obtain a relation for the minimum increase of fracture toughness required to locally arrest a fracture as a function of the dimensionless ratio of the dissipated energies (viscous versus fracture) when the fracture has just reached the heterogeneity. We obtain relations for the full parametric space covering both toughness and viscous-dominated regimes. Fully coupled numerical simulations of hydraulic fracture growth confirm the scaling relations.